how do I do so?

on top of your Pets page is a link to Adopt R Us

You can also head to the adoption center section of the forums if you want to be more choosy about who gets to adopt your pets.

if you want to abandon your pets to the pound, you can go to your pets page, click the little drop-down arrow at the upper right of the pet you want to abandon, then click "abandon." this will take you to a page where you can confirm that you want to abandon that pet. remember this will delete any items attached to the pet such as its minion or treasure chest items.

if you want to decide who adopts your pets, you can make a thread in the adoption center subforum specifying which pets are available to adopt.